Unidirectional Composite Lamina Research Articles

Numerical investigations of microscopic characteristic influences on the mechanical properties of polymer‐matrix composites

In this study, an isoparametric micro‐mechanical model is developed to study the failure behaviors under biaxial loadings for composites with different fiber arrangements. For validating the method, the numerical results of the unidirectional (UD) composite lamina with consideration of two different failure criteria (the constituent failure criterion and UD failure criterion) are compared with the experimental results. On this basis, the fiber arrangements and fiber off‐axis angles influence on the failure envelopes for the UD composite lamina are studied. Furthermore, the failure strength of a typical composite laminates is also investigated. The results show that the failure strength of composite laminates is closely dependent on the fiber arrangements. Compared with the hexagonal packing, the square diagonal packing provides the higher failure strengths. POLYM. COMPOS., 38:2734–2742, 2017. © 2015 Society of Plastics Engineers

Unidirectional fiber-reinforced composite laminae: Homogenization and localization

An algorithm for the computation of the homogenized material properties of unidirectional fiber-reinforced laminae is described. The method of extraction is such that superconvergence is realized. It is shown that the homogenized material properties are substantially independent of the number of RVEs. An algorithm for the determination of the micromechanical solution over an RVE (localization) is described and the conditions that predictors of failure initiation must satisfy are stated.

Numerical evaluation of the coefficients of thermal expansion of fibers in composite materials using a lamina-scale cost function with quasi-analytical gradients

In this work, the coefficients of thermal expansion (CTEs) of fibers in composite materials that contain microstructures are numerically evaluated using a lamina-scale cost function with quasi-analytical gradients. To consider the effects of fiber arrangements and local defects, such as interface debonding and voids, a variety of representative volume elements are modeled with a number of finite element meshes. Then, the CTEs of fibers are evaluated by minimizing a lamina-scale cost function that represents the difference between the measured CTEs and the computed CTEs by means of a computational homogenization scheme for the composite lamina. The descent direction of the cost function is obtained using quasi-analytical gradients that take partial derivatives from prediction models, such as the Schapery model and Hashin model defined in an explicit manner, which accelerates the minimization procedure. To verify the performance of the proposed scheme in terms of accuracy and efficiency, the CTEs of constituents calculated using the proposed scheme in a unidirectional composite lamina are compared with experimental values reported in the literature. Furthermore, the convergence behavior of the proposed scheme with quasi-analytical gradients is also investigated and compared with other minimization methods.

Large Strain Four-Point Bending of Thin Unidirectional Composites

A large deformation four-point bending fixture was used to test thin unidirectional composite laminas primarily used in strain energy deployable space structures. The tests allowed investigation of the large strain elastic constitutive behavior of two aerospace-grade intermediate modulus carbon fibers, a high modulus carbon fiber, and a structural glass fiber. Thermoset plastic coupons reinforced with these fibers and ranging in thickness from 0.1 to 0.5 mm were tested. A nonlinear empirical constitutive model was used to represent fiber axial tensile and compressive behavior and through a structural model, predict coupon flexural response and estimate constitutive model parameters. Intermediate modulus carbon fibers were found to be significantly nonlinear with modulus linearly increasing with strain. At failure, the fiber tangent modulus in tension was 2 to 3.1 times higher than in compression. The modulus of glass fibers was essentially constant. High modulus carbon fibers exhibited a more complex response with flexural stiffness initially slightly increasing followed by a moderate reduction in stiffness and finally, a sharp reduction in stiffness and failure.

Estimate of compressive strength of an unidirectional composite lamina using cross-ply and angle-ply laminates

In this work has been estimated the compressive strength of a unidirectional lamina of a carbon/epoxy composite material, using the cross-ply and angle-ply laminates. Over the years various methods have been developed to deduce compressive properties of composite materials reinforced with long fibres. Each of these methods is characterized by a specific way of applying load to the specimen. The method chosen to perform the compression tests is the Wyoming Combined Loading Compression (CLC) Test Method, described in ASTM D 6641 / D 6641M-09. This method presents many advantages, especially: the load application on the specimen (end load combined with shear load), the reproducibility of measurements and the experimental equipment quite simplified. Six different laminates were tested in compressive tests. They were realized by the same unidirectional prepreg, but with different stacking sequences: two cross-ply [0/90]ns, two angle-ply [0/90/±45]ns and two unidirectional laminates [0]ns and [90]ns. The estimate of the compressive strength of the unidirectional laminates at 0°, was done by an indirect analytical method, developed from the classical lamination theory, and which uses a multiplicative parameter known as Back-out Factor (BF). The BF is determined by using the experimental values obtained from compression tests.

Underwater Impulsive Loading-Induced Dynamic Failures of Monolithic Composite Panel

Designing light-weight high-performance materials which can sustain high impulsive loadings is of great interest to marine applications. In this study, a finite element fluid-structure interaction model is developed to understand the deformation and failure mechanisms of both monolithic and sandwich composite panels. Fiber (E-glass fiber) and matrix (vinylester resin) damage and degradation in individual unidirectional composite laminas are modeled with Hashin’s model. The delamination between laminas is modeled by developing a strain rate sensitive cohesive law. The deformation of the core (H250 PVC foam) in sandwich panels is modelled as a crushable foam plasticity model with volumetric hardening and strain rate sensitivity as well. The deformation history, fiber/matrix damage patterns in laminas, and inter-lamina delamination in both monolithic and sandwich composite panels are identified and compared with the experimental observations. The model suggests that the foam plays an important role in improving the performance of the sandwich panels by suppressing the transmitted impulsive acting on the back-sheets.

Modelling fibre–matrix debonding under biaxial loading

In the present work, a model for fibre–matrix debonding initiation under the biaxial loading condition (plane tension combined with out of plane shear) is proposed. The model is developed within the frame of Finite Fracture Mechanics and it is capable of predicting the critical stress value for the onset of debonding and the length of the initial defect. A parametric analysis is carried out to understand the influence of the main geometric and interface parameters on the critical debonding stress, which is found to be strongly dependent on the fibre radius. Satisfactory agreement with experimental data from the literature suggests that this approach, suitably adapted, might also be applied in the case of a unidirectional composite lamina, representing a very useful tool for modelling composite material behaviour under multiaxial loading conditions.

Damage initiation and evolution in glass/epoxy tubes subjected to combined tension–torsion fatigue loading

The matrix-dominated behaviour of unidirectional composite laminae subjected to multiaxial fatigue loading was extensively investigated. Tubular specimens with three different lay-up ([90n], [0F/90U,3] and [0F/90U,3/0F]) were tested under combined tension/torsion loadings. Attention was focused on the initiation and propagation of cracks in the 90° layers, and fatigue data are presented in terms of S–N curves (for crack initiation) and Paris-like curves (for crack propagation) under several biaxiality ratios. Damage onset and evolution have been found to be strongly affected by the multiaxial loading condition, showing a particularly detrimental effect of the shear stress component. SEM investigations on the fracture surfaces confirmed a strong dependence also of the microscopic damage modes on the local multiaxial stress state.

Bio-inspired composite structures subjected to underwater impulsive loading

Designing lightweight high-performance materials that can sustain high impulsive loadings is of great interest to marine and civil applications. When designing tough, strong new materials from relatively weak components, mimicking structures from nature can be a highly promising strategy, as illustrated by nacre from red abalone shells. One of nacre’s most impressive features is its ability to laterally spread damage and dissipate energy over millimetre length scales at crack tips and other defects. In this work, a composite panel is redesigned to mimic nacre’s microstructure. The bio-inspired composite panel and the original composite structure, which have identical areal mass, are subjected to an underwater impulsive loading scenario. Their performances are compared numerically in terms of damage and deflection. A finite element fluid–structure interaction model is developed to capture the water impact on E-glass/vinylester composite facets and to provide insights into the deformation modes and failure mechanisms. Damage and degradation in individual unidirectional composite laminas are simulated using Hashin’s composite damage model. The delamination between laminas is modelled by a bilinear cohesive model. Results interpreted from this numerical study will be used as guidance for the future manufacturing and experimental characterisation of bio-inspired composite structures.

An experimental/numerical investigation into the main driving force for crack propagation in uni-directional fibre-reinforced composite laminae

This paper presents an enriched finite element method to simulate the growth of cracks in linear elastic, aerospace composite materials. The model and its discretisation are also validated through a complete experimental test series. Stress intensity factors are calculated by means of an interaction integral. To enable this, we propose application of (1) a modified approach to the standard interaction integral for heterogeneous orthotropic materials where material interfaces are present; (2) a modified maximum hoop stress criterion is proposed for obtaining the crack propagation direction at each step, and we show that the “standard” maximum hoop stress criterion which had been frequently used to date in literature, is unable to reproduce experimental results. The influence of crack description, material orientation along with the presence of holes and multi-material structures are investigated. It is found, for aerospace composite materials with E1E2 ratios of approximately 10, that the material orientation is the driving factor in crack propagation. This is found even for specimens with a material orientation of 90°, which were previously found to cause difficulty in both damage mechanics and discrete crack models e.g. by the extended finite element method (XFEM). The results also show the crack will predominantly propagate along the fibre direction, regardless of the specimen geometry, loading conditions or presence of voids.

Three-dimensional numerical modeling of composite panels subjected to underwater blast

Designing lightweight high-performance materials that can sustain high impulsive loadings is of great interest for marine applications. In this study, a finite element fluid–structure interaction model was developed to understand the deformation and failure mechanisms of both monolithic and sandwich composite panels. Fiber (E-glass fiber) and matrix (vinylester resin) damage and degradation in individual unidirectional composite laminas were modeled using Hashin failure model. The delamination between laminas was modeled by a strain-rate sensitive cohesive law. In sandwich panels, core compaction (H250 PVC foam) is modeled by a crushable foam plasticity model with volumetric hardening and strain-rate sensitivity. The model-predicted deformation histories, fiber/matrix damage patterns, and inter-lamina delamination, in both monolithic and sandwich composite panels, were compared with experimental observations. The simulations demonstrated that the delamination process is strongly rate dependent, and that Hashin model captures the spatial distribution and magnitude of damage to a first-order approximation. The model also revealed that the foam plays an important role in improving panel performance by mitigating the transmitted impulse to the back-side face sheet while maintaining overall bending stiffness.

Geometric modelling of kink banding in laminated structures

An analytical model founded on geometric and potential energy principles for kink band deformation in laminated composite struts is presented. It is adapted from an earlier successful study on confined layered structures that was formulated to model kink band formation in the folding of geological layers. This study's principal aim was to explore the underlying mechanisms governing the kinking response of flat, laminated components comprising unidirectional composite laminae. A pilot parametric study indicates that the key features of the mechanical response are captured well and that quantitative comparisons with experiments presented in the literature are highly encouraging.

Mechanics of Composite Delamination under Flexural Loading

The mechanics of interface delamination in CFRP composite laminates is examined using finite element method. For this purpose a 12-ply CFRP composite, with a total thickness of 2.4 mm and anti-symmetric ply sequence of [45/-45/45/0/-45/0/0/45/0/-45/45/-45] is simulated under three-point bend test setup. Each unidirectional composite lamina is treated as an equivalent elastic and orthotropic panel. Interface behavior is defined using damage, linear elastic constitutive model and employed to describe the initiation and progression of delamination during flexural loading. Complementary three-point bend test on CFRP composite specimen is performed at crosshead speed of 2 mm/min. The measured load-deflection response at mid-span location compares well with predicted values. Interface delamination accounts for up to 46.7 % reduction in flexural stiffness from the undamaged state. Delamination initiated at the center mid-span region for interfaces in the compressive laminates while edge delamination started in interfaces with tensile flexural stress in the laminates. Anti-symmetric distribution of the delaminated region is derived from the corresponding anti-symmetric ply sequence in the CFRP composite. The dissipation energy for edge delamination is greater than that for internal center delamination. In addition, delamination failure process in CFRP composite can be described by an exponential rate of fracture energy dissipation under monotonic three-point bend loading.

MODELING DYNAMIC FRACTURE AND DAMAGE IN A FIBER-REINFORCED COMPOSITE LAMINA WITH PERIDYNAMICS

We propose a peridynamic formulation for a unidirectional fiber-reinforced composite lamina based on homogenization and mapping between elastic and fracture parameters of the micro-scale peridynamic bonds and the macro-scale parameters of the composite. The model is then used to analyze the splitting mode (mode II) fracture in dynamic loading of a 0 ◦ lamina. Appropriate scaling factors are used in the model in order to have the elastic strain energy, for a fixed nonlocal interaction distance (the peridynamic horizon), match the classical one. No special criteria for splitting failure are required to capture this fracture mode in the lamina. Convergence studies under uniform grid refinement for a fixed horizon size (m-convergence) and under decreasing the peridynamic horizon ( -convergence) are performed. The computational results show that the splitting fracture mode obtained with peridynamics compares well with experimental observations. Moreover, in the limit of the horizon going to zero, the maximum crack propagation speed computed with peridynamics approaches the value obtained from an analytical classical formulation for the steady-state dynamic interface debonding found in the literature.

A micro-kink theory for determination of shear modulus of a unidirectional composite lamina

A hitherto unavailable concept of fiber micro-kink responsible for microscopic shear damage is introduced. Fiber micro-kinking is caused by crystallite disorientations, as detected by the Raman and X-ray measurements, inside a carbon fiber. In addition, the fibers themselves, constituting a unidirectional composite lamina, may contain micro-flaws such as fiber misalignment. The matrix material is assumed to be linear elastic. A mechanistic (as opposed to empirical) approach for derivation of the constitutive relation in shear, based on the concept of micro-kinking (caused by crystallite disorientations) and fiber misalignment, is developed. This is the shear counterpart of the micro-cracking theory for damage assessment of composites under tension. An expression for the nonlinear shear modulus is derived based on the assumption of uniform distribution of micro-kinks and fiber misalignment defects.

Composite materials non-linear modelling for long fibre-reinforced laminates: Continuum basis, computational aspects and validations

An innovative computational methodology is proposed for modelling the material non-linear mechanical behaviour of FRP structures. To model a single unidirectional composite lamina, a serial–parallel (SP) continuum approach has been developed assuming that components behave as parallel materials in the fibres alignment direction and as serial materials in orthogonal directions. The model is based on the appropriate management of the constitutive models of the component materials, by making use of suitable ‘closure equations’ that characterize the composite micro-mechanics [Rastellini F. Modelización numérica de la no-linealidad constitutiva de laminados compuestos. PhD thesis. ETSECCPB, Politechnical University of Catalonia, Barcelona, March, 2006. [in Spanish]]. Classical lamination theory is combined with the SP model to describe multidirectional laminates. The methodology is validated through several numerical analyses, which are contrasted against benchmark tests and experimental data taken from the world-wide failure exercise [Hinton MJ, Soden PD. Predicting failure in composite laminates: The background to the exercise. Comp Sci Technol 1998; 58:1001–10].

Time-dependent Microcracking Detected in a Rubber-toughened Carbon-epoxy Composite by the Modal Acoustic Emission Method

A method of modal acoustic emission monitoring and waveform analysis is developed as a means for tracking two of the primary damage mechanisms in unidirectional composite lamina, matrix-cracking and fiber–matrix debonding. Unidirectional 30, 45 and 90° coupons of a rubber-toughened carbon-epoxy are monitored in this way for various loading histories. A method of comparing waveforms from different samples is proposed in order to establish the similarity of microcracking regardless of fiber direction. Histograms of waveform energy are used as a measure of average arrested crack length versus stress level. Larger faster cracks will emit more energy. Finally, an interpretation of the AE data is given based on an initial population of existing flaws where a cumulative distribution function (CDF) of microcracking is defined and used to study effects of stress history.

Specific Damping Capacity of Multiphase Unidirectional Hybrid Fiber Composites

Modeling and analysis on the specific damping capacity (SDC) of a unidirectional hybrid fiber composite lamina have been presented in this paper. In an attempt to refine the SDC analysis for the case of hybrid composites a new unit cell has been identified. Idealization of the proposed unit cell introduces a fiber-matrix interphase into the hybrid composite damping model. Explicit lamina level SDC equations are derived using the strain energy method. The validity and the advantages of the present method have also been demonstrated by performing numerical simulations for conventional as well as shape memory alloy (SMA) hybrid fiber composites.

Statistical model for multiaxial fatigue behavior of unidirectional plies

A statistical model is developed for the prediction of the fatigue life of unidirectional composite laminae subjected to multiaxial fatigue loading. This model is based on the experimental data for the fatigue behavior of those laminae subjected to uniaxial fatigue loading. The method is based on the extension of the generalized residual material property degradation model previously developed to describe fatigue behavior of composite materials under a wide range of stress ratios, combined with the statistical nature of static and fatigue failure of fiber-reinforced composites. The distribution function of fatigue life is determined in terms of the distribution function of static strength of the composite laminae in different loading modes, which is considered to be stochastic in nature. The fatigue life and fatigue strength of unidirectional composite laminae under any multiaxial fatigue loading are evaluated statistically by using the fatigue behavior of the laminae under uniaxial loading in longitudinal, transverse and in-plane shear directions, which is determined experimentally through material characterization. The application of the statistical model to evaluation of fatigue life and residual strength of unidirectional composite laminae subjected to biaxial fatigue loading shows good agreement with the corresponding experimental data.

Theoretical and Experimental Investigation of Progressive Failure of Woven Composite Panels

Progressive failure of laminated panels containing stacks of unidirectional non-woven composite laminae has been widely studied in recent years. However, there are few reports about the progressive failure analysis of woven composite panels. The present paper provides a methodology for the progressive failure analysis of such woven composite panels under high transverse pressure. The method incorporates the results from micro-structural analysis of a woven composite unit [1] into the macro analysis of the woven composite panel. The effect of stress concentrations due to interlacing and undulation of the woven fabrics on the strength of the material is considered. The Hashin failure criterion is used in the analysis. Three types (two woven and one non-woven) of composite panels are analysed as examples and the predicted results are compared with tests on panels. Good agreement is demonstrated.